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Национальный исследовательский университет «МИЭТ»

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Contents

5.4Algorithms of Linear Filtering and Extrapolation under Fixed Sample

Size of Measurements 156

5.4.1Optimal Parameter Estimation Algorithm by Maximal Likelihood

Criterion for Polynomial Target Track: A General Case...........

157

5.4.2Algorithms of Optimal Estimation of Linear Target Track

Parameters.........................................................................................

159

5.4.3Algorithm of Optimal Estimation of Second-Order Polynomial

Target Track Parameters	162
5.4.4 Algorithm of Extrapolation of Target Track Parameters..................	166

5.4.5Dynamic Errors of Target Track Parameter Estimation Using

Polar Coordinate System 168

5.5 Recurrent Filtering Algorithms of Undistorted Polynomial Target
Track Parameters			170
5.5.1	Optimal Filtering Algorithm Formula Flowchart.............................		170
5.5.2	Filtering of .....................................Linear Target Track Parameters		174
5.5.3	Stabilization ..........................Methods for Linear Recurrent Filters		177
	5.5.3.1 Introduction of Additional Term into Correlation
	..........................................	Matrix of Extrapolation Errors	178
	5.5.3.2 .......Introduction of Artificial Aging of Measuring Errors		179
	5.5.3.3 ............................................................	Gain Lower Bound	179
5.6 Adaptive Filtering ......Algorithms of Maneuvering Target Track Parameters			179
5.6.1	Principles of Designing the Filtering Algorithms
	of Maneuvering Target Track Parameters		179
	5.6.1.1 ...................................................................	First Approach	180
	5.6.1.2 ...............................................................	Second Approach	181
	5.6.1.3 .................................................................	Third Approach	181
5.6.2	Implementation of Mixed Coordinate Systems under Adaptive
	Filtering.............................................................................................		181
5.6.3	Adaptive Filtering Algorithm Version Based on Bayesian
	Approach in Maneuvering Target		186
5.7 Logical Flowchart ........of Complex Radar Signal Reprocessing Algorithm			192
5.8 Summary and Discussion...............................................................................			193
References.................................................................................................................			199
Chapter 6 Principles of Control Algorithm Design for Complex Radar System
Functioning at Dynamical ..............................................................................Mode			201
6.1 Configuration and ...........................Flowchart of Radar Control Subsystem			202
6.2 Direct Control of .............................Complex Radar Subsystem Parameters			207
6.2.1	Initial Conditions...............................................................................		207
6.2.2	Control under Directional Scan in Mode of Searched
	New Targets...............................................................................		207
6.2.3	Control Process under Refreshment of Target in Target
	Tracing Mode....................................................................................		211
6.3 Scan Control in New ................................................Target Searching Mode			213
6.3.1	Problem Statement .....and Criteria of Searching Control Optimality		213
6.3.2	Optimal Scanning ...........Control under Detection of Single Target		214
6.3.3	Optimal Scanning Control under Detection of Unknown
	Number of .............................................................................Targets		215
6.3.4	Example of Scanning Control Algorithm in Complex Radar

Systems under Aerial Target Detection and Tracking 219

x		Contents
6.4	Power Resource Control under Target Tracking............................................	222
	6.4.1 Control Problem Statement...............................................................	222
	6.4.2 Example of Control Algorithm under Target Tracking Mode..........	223
	6.4.3 Control of Energy Expenditure under Accuracy Aligning...............	226
6.5	Distribution of Power Resources of Complex Radar System under
	Combination of Target Searching and Target Tracking Modes	228
6.6	Summary and Discussion...............................................................................	231
References.................................................................................................................		233

Part II Design Principles of Computer System for Radar Digital Signal Processing and Control Algorithms

Chapter 7 Design Principles of Complex Algorithm Computational Process
in Radar Systems....................................................................................................			237
7.1	Design Considerations....................................................................................		237
	7.1.1	Parallel General-Purpose Computers................................................	238
	7.1.2	Custom-Designed Hardware.............................................................	239
7.2	Complex Algorithm Assignment....................................................................		241
	7.2.1 Logical and Matrix Algorithm Flowcharts.......................................		241
	7.2.2	Algorithm Graph Flowcharts............................................................	243
	7.2.3 Use of Network Model for Complex Algorithm Analysis................		246
7.3	Evaluation of Work Content of Complex Digital Signal Processing

Algorithm Realization by Microprocessor Subsystems 249

7.3.1	Evaluation of Elementary Digital Signal Processing
	Algorithm Work Content...................................................................	249
7.3.2	Definition of Complex Algorithm Work Content Using
	Network Model..................................................................................	250
7.3.3	Evaluation of Complex Digital Signal Reprocessing Algorithm
	Work Content in Radar System	252
7.4 Paralleling of Computational Process............................................................		257
7.4.1	Multilevel Graph of Complex Digital Signal Processing Algorithm......	257
7.4.2	Paralleling of Linear Recurrent Filtering Algorithm
	Macro-Operations.............................................................................	263
7.4.3	Paralleling Principles of Complex Digital Signal Processing
	Algorithm by Object Set	265
7.5 Summary and Discussion...............................................................................		267
References.................................................................................................................		271
Chapter 8 Design Principles of Digital Signal Processing Subsystems Employed
by a Complex Radar System.....................................................................................		273

8.1Structure and Main Engineering Data of Digital Signal Processing

Subsystems		273
8.1.1	Single-Computer Subsystem.............................................................	273
8.1.2	Multicomputer Subsystem.................................................................	276
8.1.3 Multimicroprocessor Subsystems for Digital Signal Processing......		278

8.1.4Microprocessor Subsystems for Digital Signal

Processing in Radar...........................................................................

280

Contents	xi
8.2 Requirements for Effective Speed of Operation............................................	282
8.2.1 Microprocessor Subsystem as a Queuing System.............................	282
8.2.2 Functioning Analysis of Single-Microprocessor Control

Subsystem as Queuing System 285

	8.2.3 Specifications for Effective Speed of Microprocessor
	Subsystem Operation.........................................................................	289
8.3	Requirements for RAM Size and Structure...................................................	293
8.4	Selection of Microprocessor for Designing the Microprocessor Subsystems......	295

8.5Structure and Elements of Digital Signal Processing and Complex

Radar System Control Microprocessor Subsystems 296

8.6High-Performance Centralized Microprocessor Subsystem for Digital

		Signal Processing of Target Return Signals in Complex Radar Systems		299
	8.7	Programmable Microprocessor for Digital Signal Preprocessing
		of Target Return Signals in Complex Radar Systems		301
	8.8	Summary and Discussion...............................................................................		302
	References.................................................................................................................			306
Chapter 9	Digital Signal Processing Subsystem Design (Example)..........................................			309
	9.1	General Statements.........................................................................................		309
	9.2	Design of Digital Signal Processing and Control Subsystem Structure.........		310
		9.2.1	Initial Statements...............................................................................	310
		9.2.2	Main Problems of Digital Signal Processing
			and Control Subsystem...................................................................	311
		9.2.3	Central Computer System Structure for Signal Processing
			and Control........................................................................................	314
	9.3	Structure of Coherent Signal Preprocessing Microprocessor Subsystem......		315
	9.4	Structure of Noncoherent Signal Preprocessing Microprocessor Subsystem.......		318
		9.4.1	Noncoherent Signal Preprocessing Problems...................................	318
		9.4.2	Noncoherent Signal Preprocessing Microprocessor Subsystem
			Requirements.....................................................................................	321
	9.5	Signal Reprocessing Microprocessor Subsystem Specifications....................		322
	9.6	Structure of Digital Signal Processing Subsystem.........................................		325
	9.7	Summary and Discussion...............................................................................		327
	References.................................................................................................................			329
Chapter 10	Global Digital Signal Processing System Analysis...................................................			331
	10.1	Digital Signal Processing System Design......................................................		331
		10.1.1	Structure of Digital Signal Processing System.................................	331
		10.1.2	Structure and Operation of Nontracking MTI..................................	332
		10.1.3	MTI as Queuing System....................................................................	335
	10.2	Analysis of “n – 1 – 1” MTI System..............................................................		339
		10.2.1	Required Number of Memory Channels...........................................	339
		10.2.2	Performance Analysis of Detector–Selector.....................................	340
		10.2.3	Analysis of MTI Characteristics.......................................................	343
	10.3	Analysis of “n – n – 1” MTI System..............................................................		344
	10.4	Analysis of “n – m – 1” MTI System..............................................................		345
	10.5	Comparative Analysis of Target Tracking Systems.......................................		347
	10.6	Summary and Discussion...............................................................................		349
	References.................................................................................................................			349

xii		Contents
Part III Stochastic Processes Measuring in Radar Systems
Chapter 11 Main Statements of Statistical Estimation Theory...................................................			353
11.1	Main Definitions and Problem Statement......................................................		353
11.2	Point Estimate and Its Properties...................................................................		356
11.3	Effective Estimations.....................................................................................		358
11.4	Loss Function and Average Risk....................................................................		359
11.5	Bayesian Estimates for Various Loss Functions............................................		362
	11.5.1	Simple Loss Function........................................................................	363
	11.5.2 Linear Module Loss Function...........................................................		364
	11.5.3	Quadratic Loss Function...................................................................	365
	11.5.4	Rectangle Loss Function...................................................................	366
11.6	Summary and Discussion...............................................................................		366
References.................................................................................................................			368
Chapter 12 Estimation of Mathematical Expectation..................................................................			369
12.1	Conditional Functional...................................................................................		369
12.2	Maximum Likelihood Estimate of Mathematical Expectation.....................		373
12.3	Bayesian Estimate of Mathematical Expectation: Quadratic
	Loss Function		381
	12.3.1 Low Signal-to-Noise Ratio (ρ2 1).................................................		383
	12.3.2 High Signal-to-Noise Ratio (ρ2 1).................................................		385
12.4	Applied Approaches to Estimate the Mathematical Expectation..................		386
12.5	Estimate of Mathematical Expectation at Stochastic Process Sampling.......		397
12.6	Mathematical Expectation Estimate under Stochastic Process
	Amplitude Quantization		408
12.7	Optimal Estimate of Varying Mathematical Expectation of Gaussian
	Stochastic Process		413
12.8	Varying Mathematical Expectation Estimate under Stochastic Process
	Averaging in Time		422
12.9	Estimate of Mathematical Expectation by Iterative Methods........................		427
12.10	Estimate of Mathematical Expectation with Unknown Period......................		430
12.11	Summary and Discussion...............................................................................		436
References.................................................................................................................			439
Chapter 13 Estimation of Stochastic Process Variance...............................................................			441
13.1	Optimal Variance Estimate of Gaussian Stochastic Process.........................		441
13.2	Stochastic Process Variance Estimate under Averaging in Time..................		449
13.3	Errors under Stochastic Process Variance Estimate......................................		455
13.4	Estimate of Time-Varying Stochastic Process Variance................................		460
13.5	Measurement of Stochastic Process Variance in Noise.................................		468
	13.5.1 Compensation Method of Variance Measurement............................		468
	13.5.2	Method of Comparison.....................................................................	473
	13.5.3 Correlation Method of Variance Measurement.................................		476
	13.5.4 Modulation Method of Variance Measurement................................		478
13.6	Summary and Discussion...............................................................................		484
References.................................................................................................................			486

Contents				xiii
Chapter 14	Estimation of Probability Distribution and Density Functions
	of Stochastic Process............................................................................................			487
	14.1	Main Estimation Regularities........................................................................		487
	14.2	Characteristics of Probability Distribution Function Estimate......................		491
	14.3	Variance of Probability Distribution Function Estimate...............................		495
		14.3.1	Gaussian Stochastic Process.............................................................	495
		14.3.2	Rayleigh Stochastic Process..............................................................	499
	14.4	Characteristics of the Probability Density Function Estimate.......................		504
	14.5	Probability Density Function Estimate Based on Expansion in Series
		Coefficient Estimations		509
	14.6	Measurers of Probability Distribution and Density Functions:
		Design Principles		514
	14.7	Summary and Discussion...............................................................................		520
	References.................................................................................................................			521
Chapter 15	Estimate of Stochastic Process Frequency-Time Parameters...................................			523
	15.1	Estimate of Correlation Function...................................................................		523
	15.2	Correlation Function Estimation Based on Its Expansion in Series...............		531
	15.3	Optimal Estimation of Gaussian Stochastic Process Correlation
		Function Parameter		539
	15.4	Correlation Function Estimation Methods Based on Other Principles..........		554
	15.5	Spectral Density Estimate of Stationary Stochastic Process.........................		561
	15.6	Estimate of Stochastic Process Spike Parameters..........................................		570
		15.6.1 Estimation of Spike Mean.................................................................		571
		15.6.2 Estimation of Average Spike Duration and Average Interval
			between Spikes..................................................................................	575
	15.7	Mean-Square Frequency Estimate of Spectral Density.................................		579
	15.8	Summary and Discussion...............................................................................		581
	References.................................................................................................................			582

Preface

The essential task in radar systems is to find an appropriate solution to the problems related to robust signal processing and definition of signal parameters. There are now a number of books and papers published in journals devoted to signal processing in noise in radar systems, but many key issues remain unsolved. New approaches to these problems allow us not only to summarize investigations but also to derive better quality of robust signal processing in noise in radar systems.

This book addresses the problems of robust signal processing in complex radar systems (CRSs) based on the generalized approach to signal processing in noise. The generalized approach to signal processing in noise is proposed based on a seemingly abstract idea: the introduction of an additional noise source that does not carry any information about the signal to improve the qualitative performance of CRSs. Theoretical and experimental studies lead to the conclusion that the proposed generalized approach to signal processing in noise in CRSs allows formulating a decision-making rule based on the determination of the jointly sufficient statistics of the mean and variance of the likelihood function. The use of classical and modern signal processing approaches allows us to define only the sufficient statistic of the mean of the likelihood function (or functional).

The presence of additional information about the statistical characteristics of the likelihood function leads to better qualitative performances of robust signal processing in CRSs in comparison with optimal signal processing algorithms of classical and modern theories. The generalized approach to signal processing allows us to extend the well-known boundaries of potential noise immunity set up by classical and modern signal processing theories. The use of CRSs based on the generalized approach to signal processing in noise allows us to obtain better detection performances, particularly in comparison with CRSs constructed on the basis of optimal and asymptotic optimal signal processing algorithms of classical and modern signal processing theories.

To better understand the fundamental statements and concepts of the generalized approach, the reader is invited to consult my earlier books: Signal Processing in Noise: A New Methodology (IEC, Minsk, 1998), Signal Detection Theory (Springer-Verlag, New York, 2001), Signal Processing Noise

(CRC Press, Boca Raton, FL, 2002), and Signal and Image Processing in Navigational Systems

(CRC Press, Boca Raton, FL, 2005).

The radar system is an important element in the field of electrical engineering. In university engineering courses, in general, the emphasis is usually on the basic tools used by the electrical engineer, such as circuit design, signals, solid state, digital processing, electronic devices, electromagnetics, automatic control, microwaves, and so on. In the real world of electrical engineering practice, however, these are only techniques, piece parts, or subsystems that make up some type of system employed for a useful purpose.

There are various aspects to radar system design. However, before a new radar system can be manufactured, a conceptual design has to be made to guide the actual development, taking into consideration the requirements of the radar system that must be customerand user-friendly. Conceptual design involves identifying the characteristics of the radar system in accordance with the radar equation and related equations and the general characteristics of the subsystems such as transmitter, antenna, receiver, signal processing, etc., that might be used. A conceptual design cannot be formed without a systems approach. Another important procedure is to define the structure of computer subsystems used in the radar for the purpose of implementing modern robust signal processing algorithms.

It should be noted that there are at least two ways in which a new CRS might be produced. One method is based on exploiting the advantages of some new invention, new technique, new device, or new knowledge. The invention of the microwave magnetron early in World War II is an example.

xvi

Preface

After the magnetron appeared, radar system design was different from what it had been before. The other, and probably more common, method for conceptual radar system design is to identify the function the new radar system has to perform, examine the various approaches available to achieve the desired capability, carefully evaluate each approach, and then select the one that best meets the needs within the operational and fiscal constraints imposed. This book discusses in detail these two methods that are based on a systems approach to design radar systems.

An important task in designing CRSs is to use robust signal processing algorithms and accurate definition of signal parameters. To this end, theory and methods of experimental investigations of stochastic processes are attracted to design the CRS. The theory of statistical estimates, for example, can be used for analyzing regularities to design and construct optimal and quasi-optimal meters of statistical parameters of stochastic processes. At the same time, significant attention is paid to investigation of systematic and random errors of statistical parameter definition as a function of considered time interval and noise level.

A detailed analysis of various procedures and methods to measure and estimate the main statistical parameters of stochastic processes, such as mean (or mathematical expectation), variance, correlation (covariance) function, power spectral density, probability density functions, spikes of energy spectra, etc., is presented. Analog and discrete procedures and methods for measurements and errors, which are characteristic of these procedures and methods, are investigated. In addition, structural block diagrams of digital meters are considered. Structural block diagrams of optimal meters to define the mathematical expectation (mean), variance, and parameters of the correlation (covariance) function are discussed. The variance of estimations and biases of the earlier-mentioned parameters is measured. A procedure to measure the mathematical expectation (mean) and variance of nonstationary stochastic process under robust signal processing used in CRSs is identified. General formulas for definition of biases and variances of statistical parameter estimations are also presented for direct analytical calculation.

I would like to thank my colleagues in the field of robust signal processing in radar systems for useful discussion about the main results, in particular, Professors V. Ignatov, A. Kolyada, I. Malevich, G. Manshin, D. Johnson, B. Bogner, Yu. Sedyshev, J. Schroeder, Yu. Shinakov, A. Kara, Kyung Tae Kim, Yong Deak Kim, Yong Ki Cho, V. Kuzkin, W. Uemura, Dr. O. Drummond, and others.

I would also like to express my gratitude to my colleagues from the Department of Information Technologies and Communications, Electronics Engineering School, College of IT Engineering, Kyungpook National University (KNU), Daegu, South Korea, for useful remarks and comments and their help in completing this project.

This research was supported by the Kyungpook National University Research Fund, 2010.

AlotofcreditisalsoduetoNoraKonopka,KariBudyk,RichardTressider,SuganthiThirunavukarasu, and John Gandour as well as to the entire staff at CRC Press, Taylor & Francis Group, for their encouragement and support.

Last, but definitely not least, I would like to thank my family—my lovely wife, Elena; my sons, Anton and Dima; and my dear mom, Natali—for putting up with me during the writing of the manuscript. Without their support, this book would not have been possible!

Finally, I wish to express my lifelong, heartfelt gratitude to Dr. Peter Tuzlukov, my father and teacher, who introduced me to science.

Vyacheslav Tuzlukov

Preface

xvii

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Natick, MA, 01760-2098 USA Tel: 508-647-7000

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